Mostly, next-gen to me means "is able to do something the previous console/gen cannot".
The thing I find most next-gen about the current consoles is their ability to record video on the fly.
I remember playing PT and thinking, "hmm what was that weird message that flashed on the screen a minute ago"....and then I realized that ps4 had been recording it the whole time, so I saved the video and rewatched it and it said something like "garbled...mon nom" which means my name, in French.
I didn't believe that there was actually something to do with the mic, but I tried again, and it worked!
Another instance, I'm playing Evil Within, and I know it's clearly not next gen. Still a good game tho.
WiiU also feels really next gen to me. I love how it feels like you're looking into a window of the game world.
